What is the most important advice that the prophet Muhammad gave to his followers?

 The most significant counsel the Prophet offered to the people, in my humble opinion, is to study and recite the Quran.

But what is the difference between studying the Quran and reciting it?

You study the Quran for yourself, to educate yourself; in Arabic, it is Iqra (اقْرَأْ), thought to be God's First Commandment in the Quran (Verse# 96:1) - implies to study, read, research, reflect, educate, and so on.

When you recite, however, you do so primarily for the benefit of others, thus you read it aloud; in Arabic, this is known as Tilawa. تلاوة – the verb is Utlu (اتْلُ)

“A messenger from God, reciting ( يَتْلُو ) to them pure scriptures,” (Al Quran# 98:2).

So, the Prophet recited the Quran to mankind to preach, and himself practiced it. The same he advised his followers to do, following the Commandment of the Quran, below:

“And recite (وَاتْلُ) that which hath been revealed unto thee of the Scripture of thy Lord. There is none who can change His words, and thou wilt find no refuge beside Him.” (Al Quran#18:27, Trans-M.M Pickthall)

You may consider this alternative translation of the passage:

“And RECITE what has been revealed to you from the Book of your Lord: no one is authorized to change His Words and if you dare to make any change, you will find no refuge to protect you from Him.” (Al Quran#18:27, Trans- Farooq Malik)

Here's something to think about. We must recite the Quran to the people, not explain it to them. The apparent reason is that the Quran explains itself; one verse interprets another. God also assures us that it is simple to comprehend. Here are several verses to consider:

“And We have indeed made the Qur'an easy to understand and remember: then is there any that will receive admonition?” (Al Quran # 54:40)

“And no question do they bring to you about which We do not reveal to you the truth and the BEST EXPLANATION.” (Al Quran # 25:33; Trans- A.L. Bilal Muhammad)

God further said:

“O People! Follow what has been sent to you from your Lord, and follow no أَوْلِيَاءَ- masters/protectors/friends/guardians/patrons /idols other than Him. How seldom do you keep this in mind!” (Al Quran # 7:3)

So, we are all obligated to do the same: recite the Quran to the people in its original form, not interpretive variants or the so-called Tafseer.

Who among you is the best?

God responds in the following passage:

"Who is better in speech than the one who invites others to Allah, performs righteousness, and says, “I am among those who submit to Allah”? ( Al Quran # 41:33)